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Article Excerpt
IN HIS FAMOUS PAPER, Hicks (1935) noted the coexistence of money and assets with higher returns as the greatest challenge facing monetary theory. Since then there have been two streams of the coexistence literature. One is to rationalize the coexistence by answering to the so-called coexistence puzzle of why individuals hold money and assets with higher returns such as bonds. Many papers have addressed this question, including Andolfatto (2006), Freeman (1985), Howitt (1974), Townsend (1980), Wallace (1983), and Zhu and Wallace (2007). The other is to provide answers to the question of why a society finds it beneficial to have both money and bonds. There have been a relatively small number of papers tackling the question.
Aiyagari, Wallace, and Wright (1996) show that if money and bonds are both indivisible and its holdings are constrained to unity, illiquid bonds traded at a discount can enhance welfare by essentially enabling the smaller trades. In Kocherlakota (2002, 2003), when agents have different valuations of consumption due to unobservable idiosyncratic preference shocks, illiquid bonds can be socially beneficial by allowing agents with different liquidity needs to make intertemporal exchanges of money. (1) Using a model in the spirit of Lagos and Wright (2005), Berentsen and Waller (2007) obtain similar results in the presence of idiosyncratic preference shocks. Boel and Camera (2006) also show that illiquid bonds serve as a device to self-insure against consumption risk when agents have different consumption needs with heterogenous discount factors.
In short, the essentiality of illiquid bonds in the above models depends critically on either the indivisibility of assets or some form of the heterogeneity in preferences. However, the indivisibility of money and bonds no longer seems to be an important constraint in modern economies. It also appears that heterogeneous preferences and different intertemporal marginal rates of substitution depend crucially on the different wealth levels across agents.
The goal of this paper is to provide an answer to the same question in the context of the standard random matching model of money where the transactional constraint due to the indivisibility of assets is mitigated by allowing agents to trade lotteries over indivisible assets. The main difference is that, in our model, the welfare-enhancing role of illiquid pure discount government bonds hinges on heterogeneous preferences that are determined endogenously by a nondegenerate wealth distribution across agents.
Specifically, we consider the random matching model of Shi (1995) and Trejos and Wright (1995) augmented with the distribution of money holdings with lotteries as in Berentsen, Molico, and Wright (2002), Berentsen, Camera, and Waller (2004), Lotz, Shevchenko, and Waller (2007), and Zhu and Wallace (2007). (2) Apart from the rate of return, bonds are distinguished from money in tangibility and liquidity; a bond is a book-entry such as the U.S. government debt. That is, at the beginning of each period, the government sells the book-entry one-period nominal bonds at a discount and only a fraction of the bonds is allowed to liquidate in the following pairwise trades. With the chosen portfolio, agents are randomly matched with another.
In pairwise meetings, agents cannot commit to their future actions and their trading histories are private. Hence, no credit arrangement is possible and money as a tangible asset should be traded in exchange for goods produced in the single-coincidence meetings where the terms of trade are determined by the buyer's take-it-or-leave-it offer. At the end of a period, each bond is redeemed by a unit of money and the required interest payments are financed by the proportional tax on monetary wealth, which is equivalent to the inflation tax. Except for issuing and redeeming bonds, the government engages in neither consumption nor production. (3)
In order to examine the societal benefits of illiquid bonds relative to the money-only economy, we begin with the definition of the monetary steady state for a given discount rate of bond and its liquidity. However, the endogeneity of a nondegenerate wealth distribution rules out the analytical characterizations of a steady state. The key properties of a monetary steady state are investigated numerically with the emphasis on the role of illiquid bonds. We then search for the optimal steady state by comparing social welfare across the different monetary steady states with different bond discount rates and degrees of liquidity. The associated social welfare is measured as the ex ante discounted expected utility of a representative agent prior to the assignment of wealth according to its steady-state distribution. Three main results follow.
First, the societal benefits of illiquid bonds are driven by their two opposing effects on the welfare. One is the welfare-enhancing effect on the distribution of wealth and the other is the distortionary effect on output net of the additional "option-value-of-money" effect. (4) A higher discount rate implies a higher inflation tax on (after-trade) wealth to finance the higher interest payments. The higher inflation tax has the distortionary effect on output produced in the sense that it is to make money less valuable, so that the quantity of output produced in exchange for money will decrease. This is somewhat offset by the "option value of money" in the sense that the ability to exchange excess money balances for bonds as interest-bearing assets raises the real value of money.
With regard to the wealth distribution effect, the relatively poor with small amount of initial money balances are more likely to be "liquidity constrained" in the future, and hence choose to top-up money balances for their future consumption by purchasing nominal bonds at a discount. With a higher ratio of bond holdings to wealth, the poor decrease their current consumption, but relatively less because they can still use some fraction of the partially liquid bonds to pay for their current consumption. On the other hand, for a given option value of money, the relatively rich bear the higher inflation-tax effect on output than do the poor. Hence, the rich decrease current consumption by a relatively large amount while holding a larger fraction of wealth in money to increase the transfers of "less-valued" money in the pairwise single-coincidence meetings. (5) The end-of-period wealth of the poor then increases, whereas that of the rich decreases. As the discount on bonds increases, therefore, the wealth distribution becomes more centered so that the variance of wealth distribution decreases. The relatively large fall of consumption by the rich also decreases the consumption deviation from the first best, and hence increases welfare. However, if the discount rate on bonds exceeds a certain level, then welfare starts declining. For a sufficiently high inflation tax implied by a high bond discount rate, the distortionary effect on output dominates the welfare-enhancing distributional effect.
Second, if bonds are perfectly liquid and their discount rate is close to zero (or price is close to unity), no one holds money in the portfolio. The real allocation of this economy is almost identical to that of the money-only economy because bonds are nearly perfect substitutes for money. This is consistent with the findings in Kocherlakota (2003), Boel and Camera (2006), and Berentsen and Waller (2007). If bonds are sufficiently liquid and their discount rate is high enough, again money is not held. The implied social welfare of this economy is also close to that of the money-only economy because a strictly positive nominal interest income accrued to illiquid bonds is approximately equivalent to the proportional money creation. This is consistent with the results in Molico (2006).
Finally, there exist combinations of bond discount rate and its liquidity under which both money and illiquid nominal bonds are held in the steady state, implying higher welfare than in the money-only steady state. Nominal bonds with proper yield and illiquidity can facilitate agents' intertemporal monetary exchanges for their consumption smoothing over time. Further, the trade-off between the distortionary effect and the distributional effect of illiquid pure-discount nominal bonds implies the socially optimal or welfare-maximizing discount rate and liquidity. The positive optimal discount rate can also be interpreted as the positive optimal nominal interest rate. This is in contrast to the representative-agent cash-in-advance models where the Friedman rule of zero nominal interest rate is prescribed as the optimal monetary policy and welfare is inversely related...
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